I've seen credit cards that prohibit using their automatic car insurance on cars rented in Italy—for example, American Express*. In this case, are there any issues with renting a car in, say, Austria (or any other Schengen country), and then driving it into Italy?
* they also exclude Australia and New Zealand, but the workaround would be much more difficult for obvious reasons.
The insurance you have linked is only "Secondary" insurance to reduce your out of pocket costs for Damage to the vehicle you rent. It is NOT the insurance that you need to drive a vehicle legally.
Whenever you drive anywhere, particularly in the first world you need to make sure you have adequate liability insurance. Not doing so is both likely to be illegal and could leave you with very large bills if an accident you are liable for causes an expensive injury.
In many cases liability insurance will be included with vehicle rentals but it pays to check if it is included and if-so what the excess is and what limitations there are on countries covered.
You'd be driving uninsured in those countries, which is a criminal offense in many countries, and certainly a violation of the contract you have with the rental company.
So yes, there'd be serious problems.
Ask the rental company, they likely have their own insurance on the car and can have you covered under that for a nominal fee.
